As Secretary of State Hillary Clinton testifies on Capitol Hill Wednesday about September's terrorist attack on the U.S. mission in Benghazi, Libya, an eye-popping number of Republicans in a new Public Policy Polling said they think she faked the illnesses that caused a delay in her testimony.

Several conservatives speculated that Clinton might have faked or embellished her illness, among them former United Nations envoy John Bolton.

The poll, the results of which were provided exclusively to Business Insider, found that a near majority of Republicans agreed with Bolton. Overall, 40 percent of Republicans responding to the poll said they believed Clinton was "faking her health problems so that she doesn’t have to testify to Congress about Benghazi." But a slim majority — 41 percent — still thought she was not.

Meanwhile, 40 percent of self-identified "very conservative" voters buy into the theory, while 32 percent of that group rejects it.

Overall, the results are much more measured, as 65 percent of respondents rejected the notion that Clinton was faking her health problems. Only 22 percent thought she was. Among self-identified Independent voters, the split was 65-18 against believing the suggestion.